Robust Bilinear Probabilistic Principal Component Analysis

Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on the maximum likelihood procedure provides a probabilistic manner to implement dimension reduction. Recently, the bilinear PPCA (BPPCA) model, which assumes that the noise terms follow matrix variate Gaussian distributions, has been introduced to directly deal with two-dimensional (2-D) data for preserving the matrix structure of 2-D data, such as images, and avoiding the curse of dimensionality. However, Gaussian distributions are not always available in real-life applications which may contain outliers within data sets. In order to make BPPCA robust for outliers, in this paper, we propose a robust BPPCA model under the assumption of matrix variate t distributions for the noise terms. The alternating expectation conditional maximization (AECM) algorithm is used to estimate the model parameters. Numerical examples on several synthetic and publicly available data sets are presented to demonstrate the superiority of our proposed model in feature extraction, classification and outlier detection.

On a Logarithmic Weighted Power Distribution: Theory, Modelling and Applications

Engineers, economists, hydrologists, social scientists, and behavioural scientists often deal with data belonging to the unit interval. One of the most common approaches for modeling purposes is the use of unit distributions, beginning with the classical power distribution. A simple way to improve its applicability is proposed by the transmuted scheme. We propose an alternative in this article by slightly modifying this scheme with a logarithmic weighted function, thus creating the log-weighted power distribution. It can also be thought of as a variant of the log-Lindley distribution, and some other derived unit distributions. We investigate its statistical and functional capabilities, and discuss how it distinguishes between power and transmuted power distributions. Among the functions derived from the log-weighted distribution are the cumulative distribution, probability density, hazard rate, and quantile functions. When appropriate, a shape analysis of them is performed to increase the exibility of the proposed modelling. Various properties are investigated, including stochastic ordering (first order), generalized logarithmic moments, incomplete moments, Rényi entropy, order statistics, reliability measures, and a list of new distributions derived from the main one are offered. Subsequently, the estimation of the model parameters is discussed through the maximum likelihood procedure. Then, the proposed distribution is tested on a few data sets to show in what concrete statistical scenarios it may outperform the transmuted power distribution.

A New Truncated Muth Generated Family of Distributions with Applications

In recent years, the Muth distribution has been used for the construction of accurate statistical models, with applications in various applied fields. In this paper, we use a truncated-composed scheme to create a new unit Muth distribution, from which we motivate a more general family of continuous distributions called the truncated Muth generated family. The key benefits of this family are its analytical simplicity, connections with the exponential generated family, and flexibility conferred on any parental distribution. In particular, it improves the capability of the functions of the parental distribution, enhancing their peak, asymmetry, tail, and flatness levels, among others. The characteristics of quantile and moment measures and functions of the truncated Muth generated family are described in detail. As a concrete example, a particular distribution that extends the Weibull distribution is highlighted. In an applied part, the parameters are calculated using the maximum likelihood procedure. We use a comprehensive simulation analysis to demonstrate the accuracy of the derived estimates. The revised Weibull model is then used to fit two real-world datasets. The new model is shown to be more suited to these datasets than other competing models.

Association Between Backfat Thickness at 28 Weeks Old and Production Traits of Primiparous Landrace Sows Raised Under Tropical Conditions

Backfat thickness could reflex energy reserve of the female pigs that is required for their productivity, especially gilts that might be selected for the replacements. Therefore, phenotypic and genetic correlations between backfat thickness (BF) and production traits were estimated and considered for the possibility of using BF at pre-selective stage as an early indicator for productivity of the sow. Pedigree information, BF and body weight (BW) at 28 weeks old, age at first farrowing (AFF), transformed proportion of piglet loss at birth (tPL) and transformed weaning to first service interval (tWSI) of 806 primiparous Landrace sows were used to estimate the variance components by restricted maximum likelihood procedure with an average information algorithm for multivariate analysis. Genetic correlation between BF and BW was 0.70 ± 0.13. Both BF and BW had negative genetic correlation with AFF, but not tWSI. Unfortunately, genetic correlation estimates between tPL and other traits was unclear due to high standard error. The genetic correlation between AFF and tWSI was 0.78 ± 0.36. Besides 19.35% of sires, 26.34% of dams and 25.81% of sows had genetic ability for BF, BW, AFF and WSI above the population means. The genetic association between BF, BW, AFF and tWSI indicated the feasibility of using selection index to improve BF and BW at pre-selective stage and reduce AFF and tWSI of replacement gilt simultaneously. However, the estimation of genetic correlation between PL and other traits should be repeated in a larger population.

A Four-Parameter Extension of Burr III Distribution with Applications

In this paper, we defined and studied a new distribution called the odd exponentiated half-logistic Burr III distribution. Properties such as the linear representation of the probability density function (PDF) of the distribution, quantile function, ordinary and incomplete moments, moment generating function and distribution of the order statistic were derived. The PDF and hazard rate function were found to be capable of having various shapes, making the new distribution highly flexible. In particular, the hazard rate function can be nonincreasing, unimodal and nondecreasing. It can also have the bathtub shape among other non- monotone shapes. The maximum likelihood procedure was used to estimate the parameters of the new model. We gave two numerical examples to illustrate the usefulness and the ability of the distribution to provide better fits to a number of data sets than several distributions in existence.Keywords: Burr III distribution; maximum likelihood procedure; moments; odd exponentiated half-logistic-G family; order statistics. AbstrakPada artikel ini akan didefinisikan dan dipelajari mengenai distribusi baru yang disebut distribusi Burr III setengah logistik tereksponen ganjil. Kami menurunkan beberapa sifat dari distribusi tersebut yaitu representasi linier dari fungsi kepadatan peluang (FKP), fungsi kuantil, momen biasa dan momen tidak lengkap, fungsi pembangkit momen dan distribusi statistik terurut. Fungsi FKP dan fungsi tingkat hazard diperoleh memiliki bermacam-macam bentuk, membuat distribusi baru ini sangat fleksibel. Secara khusus, fungsi tingkat hazard dapat berupa fungsi taknaik, bermodus tunggal, bisa juga tidak turun. Selain itu, fungsi ini juga dapat berbentuk seperti bak mandi di antara bentuk-bentuk tak monoton lainnya. Prosedur kemungkinan maksimum digunakan untuk mengestimasi parameter model yang baru. Kami memberikan dua contoh numerik untuk mengilustrasikan kegunaan dan kemampuan distribusi untuk menghasilkan kesesuaian yang lebih baik pada sejumlah kumpulan data dibandingkan beberapa distribusi yang ada.Kata kunci: distribusi Burr III; prosedur kemungkinan maksimum; momen; keluarga setengah logistik-G teresponen ganjil; statistic terurut.

Odd Generalized N-H Generated Family of Distributions with Application to Exponential Model

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.

Clothing brand purchase intention through SNS

PurposeThe purpose of this paper is to investigate the intention to purchase products through clothing brands’ social network sites (SNS) based on the theory of planned behavior and uses and gratifications theory (U&G), and the moderating effects of self-image congruity (SIC).Design/methodology/approachData were collected from 1,003 followers of their favorite clothing brands’ SNS. Data analysis was performed using structural equation modeling (SEM) and multi-group SEM analysis. The models were estimated from the matrices of variances and covariances by the maximum likelihood procedure using EQS 6.1.FindingsThe results highlight the positive impact of U&G on attitude, SNS intentions and SNS use, and U&G, SNS intentions and SNS use were seen to be the main antecedents predicting purchase intentions. Furthermore, SIC was found to have moderating effects between SNS attitude and SNS intentions and between SNS intentions and SNS use.Practical implicationsThis research can help clothing brands understand the need to generate brand beliefs, and to develop contents or events to help accomplish the transition from use to purchase.Originality/valueThis research contributes to the literature by providing a better understanding of intention to use and purchase intention through clothing brands’ SNS pages.

Heritability of advertisement call properties of the Japanese quail

The objective of this study was to investigate genetic variances and covariances among features of the male Japanese quail advertisement call. Duration of the first, second and third syllable, the length of interval 1 (between the first and the second syllable), interval 2 (between the second and the third syllable) and damping (extension of the third syllable) were measured as temporal properties of the call. Spectral properties were peak frequencies of each syllable and the damping component. In this study, 1730 calls were recorded from 488 male Japanese quail. The restricted maximum likelihood procedure for repeated measurements was applied to estimate (co)variance components and genetic parameters for the examined traits. Heritability estimates of call parameters of the male Japanese quail ranged from low to high values (0.04-0.65) and they were generally higher for temporal properties than for spectral properties. Among the temporal properties of the call, the highest genetic correlation was between the first and the second syllable (0.96±0.251) while the lowest genetic correlation was between the first and the third syllable (0.03±0.231). Significant genetic correlations were generally high and positive among peak frequencies of the syllables. Despite the lack of apparent pattern, interval lengths tended to have positive correlation with spectral properties of the call, but the correlation of syllable lengths with spectral properties of the call was negative.

Two consistent estimators for the skew Brownian motion

The skew Brownian motion (SBm) is of primary importance in modeling diffusion in media with interfaces which arise in many domains ranging from population ecology to geophysics and finance. We show that the maximum likelihood procedure estimates consistently the parameter of an SBm observed at discrete times. The difficulties arise because the observed process is only null recurrent and has a singular distribution with respect to the one of the Brownian motion. Finally, using the idea of the expectation–maximization algorithm, we show that the maximum likelihood estimator can be naturally interpreted as the expected total number of positive excursions divided by the expected number of excursions given the observations. The theoretical results are illustrated by numerical simulations.